A plant can either have a smooth seed (p) or a rough seed (q). Rough seeds are recessive and smooth seeds are dominant. In a population of 100 plants, 32 of them have rough seeds.

p^2 + 2pq + q^2 = 1

a) What is q^2?

b) What is q?

c) What is p?

d) If there are 19 plants with rough seeds in a population of 100, what is the allele frequency for smooth seeds?

To calculate this, the Hardy-Weinberg principle can be used:

p² + 2pq + q² = 1 and p + q = 1

where p and q are the frequencies of the alleles (p - dominant, q - recessive), and p², q² and 2pq are the frequencies of the genotypes.

a) Since 32 plants have rough seed (recessive genotype: q²) out of 100 plants in total, then

q² = 32/100 = 0.32

b) q = √q² = √0.32 = 0.56

c) Since p + q = 1, then

p = 1 - q = 1 - 0.56 = 0.44

d) 19 plants with rough seeds (recessive genotype: q²) in a population of 100 means that q² = 19/100 = 0.19

We need to calculate p (the allele frequency for smooth seeds).

We can find q because we know q²:

q = √q² = √0.19 = 0.44

Since p + q = 1, then

p = 1 - q = 1 - 0.4 = 0.56